Nonperturbative Conditions for Local Weyl Invariance on a Curved World Sheet

Abstract

We investigate Weyl anomalies on a curved world sheet to second order in a weak field expansion. Using a local version of the exact renormalization group equations, we obtain nonperturbative results for the tachyon/graviton/dilaton system. We discuss the elimination of redundant operators, which play a crucial role for the emergence of target space covariance. Performing the operator product expansion on a curved world sheet allows us to obtain the nonperturbative contributions to the dilaton $β$ function. We find the $β$ functions, after suitable field redefinitions, to be related to a target space effective action through a $κ$ function involving derivatives. Also we can establish a nonperturbative Curci-Paffuti relation including the tachyon $β$ function.